You might want to subscribe a user that registers on your website to a MailChimp list of your choice, this can be achieved using 2 methods.
Using Profile Builder
In a paid version of Profile Builder (hobbyist or above) you can use the MailChimp add-on to add a newsletter checkbox to your registration form. Instructions about this functionality can be found here.
This works with Paid Member Subscriptions also since the two plugins are integrated with each other and you can construct the form using Profile Builder. More info about that can be found here.
This method is more powerful as it allows for extra customization and it also enables you to sync data from extra form fields with MailChimp.
Using MailChimp for WordPress
Paid Member Subscriptions Pro
Accept (recurring) payments, create subscription plans and restrict content on your website. Easily setup a WordPress membership site using Paid Member Subscriptions.Unlock PRO Features